1. (25pts) Consider a system with the following plant transfer function: Y(s) S P(s)= U(s) s+3s-3s+a a) Place a controller K(s) in front of the plant where K(s)=k+ks utilizing unity negative feedback. For what a values (both sufficient and necessary) can such a controller stabilize the system? b) Design a controller K(s) that paces the poles of the resulting closed loop system at -1, -2, and -3. c) What is the ess(t) for the closed-loop controlled system given a step input? d) What type of controller (P, PI, PD, PID, etc.) is given in part a)?